Question

I need help, arithmetic sequences always mess me up

Answer 1

Answer:

$a_{45}=399$ is the required term.

Step-by-step explanation:

We have been given an arithmetic sequence where we have a common difference which is:$d=a_2-a_1$

$d=12-3=9$

We will use the formula to find the required term:

$a_n=a+(n-1)d$

where, a is first term which is 3 and d is the common difference which is 9

and n =45 which we require to find.

$a_{45}=3+(45-1)(9)$

$a_{45}=3+396$

$a_{45}=399$.

Answer 2

Answer:

Missing term of the sequence is 399.

Step-by-step explanation:

In the given table we will try to find the sequence in terms of y and x parameters.

Since y = 3, 12, 21, 30,......... it's an arithmetic progression then we can represent nth term of this sequence as y = a + (x-1)d where a = first term, x = number of terms and d = common difference.

y = 3 + (x-1)×d = 3 + (x-1)×9 = 3 + 9x -9 = (9x - 6)

Now we have to find the term x = 45 ( 45th term)

By putting the value of x = 45 in the equation we will find the value of y.

y = 9×45 - 6 = 405 -6 = 399